Electric field switchable magnetic devices

ABSTRACT

A magnetic device may include a layer stack. The layer stack may include a first ferromagnetic layer; a non-magnetic spacer layer on the first ferromagnetic layer, where the non-magnetic spacer layer comprises at least one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr, or V; a second ferromagnetic layer on the non-magnetic spacer layer; and an oxide layer on the second ferromagnetic layer. The magnetic device also may include a voltage source configured to apply a bias voltage across the layer stack to cause switching of a magnetic orientation of the second ferromagnetic layer without application of an external magnetic field or a current. A thickness and composition of the non-magnetic spacer layer may be selected to enable a switching direction of the magnetic orientation of the second ferromagnetic layer to be controlled by a sign of the bias voltage.

This application claims the benefit of U.S. Provisional PatentApplication No. 62/645,589, titled, “ELECTRIC FIELD SWITCHABLE MAGNETICDEVICES,” filed Mar. 20, 2018, the entire content of which isincorporated herein by reference.

GOVERNMENT RIGHTS

This invention was made with government support under Grant No.HR0011-13-3-0002 awarded by the Department of Defense/Defense AdvancedResearch Projects Agency (DARPA). The government has certain rights inthe invention.

TECHNICAL FIELD

This disclosure relates to magnetic devices including magneticstructures, and more particularly, magnetic tunnel junctions.

BACKGROUND

The scaling of conventional semiconductor devices may be limited byfactors including device reliability and increased power consumption.Improvement in the performance of memory and computational devices iscontinuously pursued. Magnetic tunnel junction structures use relativeorientation of two or more magnetic layers to affect resistance of themagnetic tunnel junction structure and may be used in logic and memorydevices.

SUMMARY

In some examples, the disclosure describes a magnetic device thatincludes a layer stack. The layer stack may include a firstferromagnetic layer; a non-magnetic spacer layer on the firstferromagnetic layer, where the non-magnetic spacer layer comprises atleast one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr, or V; a secondferromagnetic layer on the non-magnetic spacer layer; and an oxide layeron the second ferromagnetic layer. The magnetic device also may includea voltage source configured to apply a bias voltage across the layerstack to cause switching of a magnetic orientation of the secondferromagnetic layer without application of an external magnetic field ora current. A thickness and composition of the non-magnetic spacer layermay be selected to enable a switching direction of the magneticorientation of the second ferromagnetic layer to be controlled by a signof the bias voltage.

In some examples, the disclosure describes a method that includescontrolling, by a write controller, a voltage source to output apositive bias voltage across a layer stack. The layer stack includes afirst ferromagnetic layer; a non-magnetic spacer layer on the firstferromagnetic layer, where the non-magnetic spacer layer comprises atleast one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr or V; a secondferromagnetic layer on the non-magnetic spacer layer; and an oxide layeron the second ferromagnetic layer. The positive bias voltage causesswitching of a magnetic orientation of the second ferromagnetic layerfrom a first direction to a second direction without application of anexternal magnetic field or a current. The method also includescontrolling, by the write controller, the voltage source to output anegative bias voltage across the layer stack. The negative bias voltagecauses switching of the magnetic orientation of the second ferromagneticlayer from the second direction to the first direction withoutapplication of an external magnetic field or a current.

In some examples, the disclosure describes a voltage controlled magneticanisotropy magnetoresistive random access memory device including alayer stack and a voltage source. The layer stack may include a firstferromagnetic layer; a non-magnetic spacer layer on the firstferromagnetic layer, where the non-magnetic spacer layer comprises atleast one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr, or V; a secondferromagnetic layer on the non-magnetic spacer layer; and an oxide layeron the second ferromagnetic layer. The voltage source may be configuredto apply a bias voltage across the layer stack to cause switching of amagnetic orientation of the second ferromagnetic layer withoutapplication of an external magnetic field or a current. A thickness andcomposition of the non-magnetic spacer layer may be selected to enable aswitching direction of the magnetic orientation of the secondferromagnetic layer to be controlled by a sign of the bias voltage.

In some examples, the disclosure describes a stochastic computing deviceincluding a random bit stream generator. The random bit stream generatorincludes a layer stack and a voltage source. The layer stack may includea first ferromagnetic layer; a non-magnetic spacer layer on the firstferromagnetic layer, where the non-magnetic spacer layer comprises atleast one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr, or V; a secondferromagnetic layer on the non-magnetic spacer layer; and an oxide layeron the second ferromagnetic layer. The voltage source may be configuredto apply a bias voltage across the layer stack to cause switching of amagnetic orientation of the second ferromagnetic layer withoutapplication of an external magnetic field or a current. A thickness andcomposition of the non-magnetic spacer layer may be selected to enable aswitching direction of the magnetic orientation of the secondferromagnetic layer to be controlled by a sign of the bias voltage.

In some examples, the disclosure describes a stochastic spiking neuralnetwork device including a magnetic device. The magnetic device includesa layer stack and a voltage source. The layer stack may include a firstferromagnetic layer; a non-magnetic spacer layer on the firstferromagnetic layer, where the non-magnetic spacer layer comprises atleast one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr, or V; a secondferromagnetic layer on the non-magnetic spacer layer; and an oxide layeron the second ferromagnetic layer. The voltage source may be configuredto apply a bias voltage across the layer stack to cause switching of amagnetic orientation of the second ferromagnetic layer withoutapplication of an external magnetic field or a current. A thickness andcomposition of the non-magnetic spacer layer may be selected to enable aswitching direction of the magnetic orientation of the secondferromagnetic layer to be controlled by a sign of the bias voltage. Insome examples, the magnetic device may be used as part or all of theneurons of the stochastic spiking neural network device.

The details of one or more examples are set forth in the accompanyingdrawings and the description below. Other features, objects, andadvantages of the disclosure will be apparent from the description anddrawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a conceptual block diagram of a layer stack that includes acomposite free layer with a synthetic antiferromagnetic structure, inaccordance with examples of the disclosure.

FIGS. 2A and 2B are conceptual diagrams illustrating examples of thelayer stack of FIG. 1 under ferromagnetic coupling andanti-ferromagnetic coupling, respectively.

FIG. 3 is a conceptual block diagram of a layer stack that includes acomposite free layer with a dual synthetic antiferromagnetic structure,in accordance with examples of the disclosure.

FIG. 4 is a conceptual block diagram of a perpendicular magnetic tunneljunction that includes a synthetic antiferromagnet free layer, inaccordance with examples of the disclosure.

FIG. 5 is a conceptual block diagram of a perpendicular magnetic tunneljunction that includes a dual synthetic antiferromagnet free layer, inaccordance with examples of the disclosure.

FIGS. 6A and 6B are conceptual diagrams illustrating examples of thelayer stack of FIG. 5 under a positive bias voltage and a negative biasvoltage, respectively.

FIG. 7 is a conceptual block diagram of a perpendicular magnetic tunneljunction that includes a dual synthetic antiferromagnet free layer and asynthetic antiferromagnet reference layer, in accordance with examplesof the disclosure.

FIG. 8A is a conceptual and schematic diagram of an exampleperpendicular magnetic tunnel junction including a dual syntheticanti-ferromagnet free layer and a reference layer.

FIG. 8B is a plot of an out-of-plane magnetic hysteresis (M-H) loop of adual p-synthetic anti-ferromagnet free layer with a stack of FePd(3nm)/Ru(1.1 nm)/FePd(3 nm)/Ta(0.8 nm)/CoFeB(1.3 nm).

FIG. 8C is a microscopy image of a 150-nm diameter perpendicularmagnetic tunnel junction pillar.

FIG. 8D is a plot illustrating magnetoresistance-applied field loops asa function of the temperature for perpendicular magnetic tunneljunctions with 150 nm diameter and synthetic antiferromagnet freelayers.

FIG. 9, is a plot of an out-of-plane magnetic hysteresis (M-H) loop of aFePd p-synthetic anti-ferromagnet free layer with a stack of FePd(3nm)/Ru(1.1 nm)/FePd(3 nm).

FIG. 10 is a plot of normalized magnetoresistance versus applied fieldfor FePd synthetic antiferromagnet perpendicular magnetic tunneljunctions with 150 and 500 nm diameter.

FIGS. 11A-11C illustrate a scanning electron microscopy image of a topview of the 350° C.-annealed FePd synthetic antiferromagnetperpendicular magnetic tunnel junction stacks with diameters rangingfrom about 35 nm to about 250 nm, an atomic force microscopy imageillustrating topography of the pillars, and a current map measured byconductive atomic force microscopy at 100 mV, respectively.

FIG. 12A is a conceptual and schematic diagram illustrating anexperimental setup for performing measurements on a perpendicularmagnetic tunnel junction using conductive atomic force microscopy, inwhich the atomic force microscopy tip is grounded and the bias voltageis applied at the bottom electrode.

FIG. 12B is a plot of minor magnetoresistance versus appliedperpendicular external magnetic field (H_(ext)) for an 100-nm diameterFePd synthetic antiferromagnet perpendicular magnetic tunnel junction atdifferent bias voltages (V_(bias)=±0.75 V, −0.1 V and −0.75 V,respectively).

FIG. 12C is a plot depicting the mean coercivity (H_(c)) of a dual SAFfree layer of a 100-nm diameter FePd synthetic antiferromagnetperpendicular magnetic tunnel junction as a function of bias voltage(V_(bias)).

FIG. 12D is a plot of effective magnetic anisotropy (K_(u,eff)) versusbias voltage (V_(bias)) and a fitted coefficient of voltage controlledmagnetic anisotropy (VCMA).

FIG. 13 is a plot depicting the mean coercivity (H_(c)) of a dual SAFfree layer as a function of the bias voltage (V_(bias)) in comparison tomean coercivity (H_(c)) of a CoFeB free layer in the CoFeB/MgO/CoFeBperpendicular magnetic tunnel junction as a function of bias voltage.

FIG. 14A is a plot of a current versus bias voltage (V_(bias)) curve(I-V curve) obtained by sweeping the bias voltage (V_(bias)) from −0.6 Vto +0.6 V for an 100-nm diameter FePd synthetic antiferromagnetperpendicular magnetic tunnel junction annealed at 350° C.

FIG. 14B illustrates plots of the bi-directional magnetization switchingby writing by a voltage and reading by current (bias voltage versus timeand current versus time), respectively, for an 100-nm diameter FePdsynthetic antiferromagnet perpendicular magnetic tunnel junction.

FIG. 15 is a plot of a current versus bias voltage (V_(bias)) curve (I-Vcurve) obtained by sweeping the bias voltage (V_(bias)) from −2.1 V to+2.1 V for a 35-nm diameter FePd synthetic antiferromagnet perpendicularmagnetic tunnel junction annealed at 400° C.

FIG. 16 is a plot of a current versus bias voltage (V_(bias)) curve (I-Vcurve) obtained by sweeping the bias voltage (V_(bias)) from −1.5 V to+1.7 V for a 40-nm diameter FePd synthetic antiferromagnet perpendicularmagnetic tunnel junction annealed at 350° C.

FIG. 17 is a conceptual diagram of a stochastic number generatorconfigured to generate a stochastic bit stream.

DETAILED DESCRIPTION

The disclosure describes perpendicular synthetic antiferromagnetic(p-SAF) structures and perpendicular magnetic tunnel junctions (p-MTJs)using these p-SAF structures. The strength and sign of magnetic couplingof these p-SAF structures may be changed and the p-MTJs with these p-SAFdescribed herein may be switched using only an applied electric field(bias voltage), without using an applied external magnetic field or anapplied current. The p-SAF structure, that includes a firstferromagnetic layer/non-magnetic layer (as a spacer)/secondferromagnetic layer/dielectric layer heterostructure, may be designedwith interfacial perpendicular magnetic anisotropy (i-PMA) materials.The i-PMA materials include a non-magnetic layer/ferromagneticlayer/dielectric layer heterostructure. The magnetic anisotropy of theferromagnetic layer may be selected so that magnetic orientation of theferromagnetic layer may be switched upon application of an electricfield (e.g., via a bias voltage) without application of an externalmagnetic field or spin current. The thickness and composition of thenon-magnetic layer of the p-SAF structure may be selected so that a signand strength of the interlayer exchange coupling (IEC) between the firstferromagnetic layer and second ferromagnetic layer may be affected byapplication of an electric field (e.g., via a bias voltage) withoutapplication of an external magnetic field or current. This may result inswitching of a magnetic orientation of the second ferromagnetic layer inresponse to application of an electric field (e.g., via a bias voltage)with a selected sign, without application of an external magnetic fieldor current. The p-SAF structure may be used as part of a p-MTJ, forexample, as a SAF free layer.

The applied electric field may modify magnetic anisotropy of theferromagnetic layer of the i-PMA structure, affect interlayer exchangecoupling between two ferromagnetic layers, or both. For example, basedon the sign of the applied bias voltage, electrons may accumulate or bedepleted at the interface between the second ferromagnetic layer and thedielectric layer. This accumulation or depletion of electrons at theinterface shifts the fermi level (E_(F)) of ferromagnetic layer,increasing or decreasing the minority spin density (d-orbitals),respectively. Increasing the minority spin density (d-orbitals) mayenhance the reflectivity of the minority spins in the non-magneticlayer/second ferromagnetic layer interface and lead to ferromagneticcoupling, while decreasing the minority spin density (d-orbitals) mayreduce the reflectivity of the minority spins in the non-magneticlayer/second ferromagnetic layer interface and lead toanti-ferromagnetic coupling. In this way, applying a bias voltage of aselected sign and sufficient magnitude can achieve switching betweenanti-ferromagnetic coupling and ferromagnetic coupling and vice versa,thus achieving switching of the p-MTJ between high and low resistancestates, without application of an external magnetic field or a current.

In some examples, the p-MTJ with p-SAF structure may be used as a memoryor logic device, for example, for a magnetoresistive random accessmemory or an all-spin logic device. By controlling the bias voltageapplied across the p-MTJ with p-SAF free layer, the sign of p-SAF can betuned and form ferromagnetic coupling or antiferromagnetic coupling,realizing the high or low resistance states for p-MTJs. This may providethe efficient way to obtain the memory or logic devices with highswitching speed and ultralow energy consumption.

In some examples, the p-MTJ with p-SAF free layer may be used as arandom bit generator, for example, for a stochastic computing device ora stochastic spiking neural network. By controlling the bias voltageapplied across the p-MTJ with p-SAF free layer, the thermal stability ofthe free layer of the MTJ may be controlled so that thermal energy atroom temperature is sufficient to cause switching the ferromagneticcoupled and anti-ferromagnetic coupled states, or the sign of p-SAF freelayer can be oscillated so that bias voltage (E-field) at roomtemperature is sufficient to cause switching the ferromagnetic coupledand anti-ferromagnetic coupled states. This may be used to producerandom bits, e.g., as part of a random bit stream for a stochasticcomputing device or a stochastic spiking neural network.

FIG. 1 is a conceptual block diagram of a layer stack 10 that includes acomposite free layer with a SAF structure, in accordance with examplesof the disclosure. Layer stack 10 includes a seed layer/first electrode12, a first ferromagnetic layer 14 on seed layer/first electrode 12, anon-magnetic layer 16 on first ferromagnetic layer 14, a secondferromagnetic layer 18 on non-magnetic layer 16, a dielectric barrierlayer 20 on second ferromagnetic layer 18, and a cap layer/secondelectrode 22 on dielectric barrier layer 20.

Seed layer/first electrode 12 may include a material selected to helpestablish a preferred growth configuration for first ferromagnetic layer14. Seed layer/first electrode 12 also may be electrically conductive tofunction as an electrode for application of a bias voltage (E-field) tolayer stack 10. In some examples, seed layer/first electrode 12 mayinclude Cr, Pt, Pd, a Cr/Pt, Cr/Pd, Cr/Ru bilayer, or the like. Forexample, seed layer/first electrode 12 may include a first layer of Cron a substrate and a second layer of Pt on the first layer of Cr. Insome examples, the first layer of Cr may be thicker than the secondlayer of Pt. For example, the first layer of Cr may define a thicknessof between about 10 nm and about 50 nm, such as 15 nm, and the secondlayer of Pt may define a thickness of between about 2 nm and about 50nm, such as about 5 nm.

First ferromagnetic layer 14 may include a ferromagnetic material. Firstferromagnetic layer 14 may have an easy magnetic axis oriented out ofthe plane of first ferromagnetic layer 14, e.g., substantiallyperpendicular to the plane of first ferromagnetic layer 14. Firstferromagnetic layer 14 may include a ferromagnetic thin film havingperpendicular magnetic anisotropy, such as FePd, FePt, CoPd, CoPt, aMn-based Heusler alloy, MnAl, MnBi, MnGaN, MnGeN, or the like. Firstferromagnetic layer 14 may define any suitable thickness, such asbetween about 1 nm and about 12 nm, such as between about 1 nm and about4 nm, or about 2 nm, or between about 3 nm and about 12 nm.

Non-magnetic layer 16 is on first ferromagnetic layer 14 and includes anon-magnetic material. Non-magnetic layer 16 is a spacer layer betweenfirst ferromagnetic layer 14 and second ferromagnetic layer 18. Thenon-magnetic material may include the materials which can generate theinterlayer exchange coupling between first ferromagnetic layer 14 andsecond ferromagnetic layer 18. The non-magnetic material may include,for example, Ru, Ir, Ta, Cr, W, Mo, V, MgO, Re, Hf, Zr or the like. Insome examples, non-magnetic layer 16 may include multiple sub-layers,such as a Ru/Ta bilayer, a Ru/Pt bilayer, an Ir/Ta bilayer, a Ru/Mg, orthe like. Non-magnetic layer 16 may define a thickness between about 0.3nm and about 5 nm, such as Non-magnetic layer 16 generates interlayerexchange coupling (IEC) between first ferromagnetic layer 14 and secondferromagnetic layer 18. The default (e.g., in the absence of a biasvoltage) IEC, whether ferromagnetic coupling or antiferromagneticcoupling, may depend at least in part upon the thickness of non-magneticlayer 16. For example, a non-magnetic layer 16 with a thickness betweenabout 0.3 nm and about 3.0 nm may cause the transition of ferromagneticcoupling or antiferromagnetic coupling between first ferromagnetic layer14 and second ferromagnetic layer 18 in the absence of a bias voltageapplied to layer stack 10. In some examples, non-magnetic layer 16 mayinclude Ru and a thickness of about 1 nm and about 2 nm, such as about1.1 nm; Ta and a thickness of between about 0.5 nm and about 2.5 nm,such as about 0.8 nm.

Further, a thickness and a composition of non-magnetic layer 16 may beselected to control the strength of the interlayer exchange couplingbetween first ferromagnetic layer 14 and second ferromagnetic layer 18.For example, the thickness and the composition of non-magnetic layer 16may be selected so that application of a bias voltage across layer stack10 resulting in switching of a magnetic orientation of secondferromagnetic layer 18.

Second ferromagnetic layer 18 is on non-magnetic layer 16 and includes aferromagnetic material. Second ferromagnetic layer 18 may have an easymagnetic axis oriented in plane or out of the plane of secondferromagnetic layer 18, e.g., substantially perpendicular to the planeof second ferromagnetic layer 18. Second ferromagnetic layer 18 mayinclude, for example, a CoFeB alloy, such as Co₂₀Fe₆₀B₂₀; a CoFe alloy,Co, Fe, a Co-based Heusler alloy, or a Mn-based Heusler alloy. Secondferromagnetic layer 18 may define any suitable thickness, such asbetween about 1 nm and about 12 nm, such as between about 1 nm and about4 nm, or about 2 nm, or between about 3 nm and about 12 nm. In someexamples, second ferromagnetic layer 18 includes a CoFeB alloy and athickness of about 1.3 nm. in some examples, second ferromagnetic layer18 may possess interfacial or bulk perpendicular magnetic anisotropy.The magnetic anisotropy of second ferromagnetic layer 18 may controlledbased on a thickness and a composition of second ferromagnetic layer 18.The thickness and composition of second ferromagnetic layer 18 may beselected so that magnetic orientation of second ferromagnetic layer 18(e.g., rather than first ferromagnetic layer 18) may be switched uponapplication of an electric field (e.g., via a bias voltage) withoutapplication of an external magnetic field or a current.

First ferromagnetic layer 14, non-magnetic layer 16, and secondferromagnetic layer 18 may define a synthetic antiferromagnet (SAF). Forexample, in the absence of a bias voltage, first ferromagnetic layer 14may be antiferromagnetically coupled to second ferromagnetic layer.

Dielectric barrier layer 20 is on second ferromagnetic layer 18 and mayinclude a suitable dielectric material, such as, for example, an oxide.Suitable oxides include MgO, AlO_(x), MgAl₂O₄, HfO_(x), or the like.Dielectric barrier layer 20 may define any suitable thickness, such asbetween about 1 nm and about 30 nm.

Cap layer/second electrode 22 is on dielectric barrier layer 20 andinclude one or more electrically conductive layers. For example, caplayer/second electrode may include a first layer including Ta and asecond layer including Ti, Au, or the like.

Cap layer/second electrode 22 and seed layer/first electrode 12 may beelectrically connected to a voltage source 24. In some examples, one orboth of cap layer/second electrode 22 or seed layer/first electrode 12may be electrically connected to voltage source 24 indirectly. Forexample, voltage source 24 may be electrically connected to a substrateon which seed layer/first electrode 12 is formed.

FIGS. 2A and 2B are conceptual diagrams illustrating examples of thelayer stack of FIG. 1 under ferromagnetic coupling andanti-ferromagnetic coupling, respectively. As shown in FIG. 2A, when anegative bias voltage is applied by voltage source 24 to seedlayer/firstelectrode 12, E_(F) is shifted upwards and electrons accumulate at theinterface of second ferromagnetic layer 18 and dielectric barrier layer20. The minority spin density (d orbitals) is enhanced and firstferromagnetic layer 14 and second ferromagnetic layer 18 areferromagnetically coupled. Further, the IEC (J₁) is positive.

As shown in FIG. 2B, when a positive bias voltage is applied by voltagesource 24 to seedlayer/first electrode 12, E_(F) is shifted downward andelectrons deplete at the interface of second ferromagnetic layer 18 anddielectric barrier layer 20. The minority spin density (d orbitals) isreduced and first ferromagnetic layer 14 and second ferromagnetic layer18 are antiferromagnetically coupled. Further, the IEC (J₁) is negative.

In some examples, a layer stack may include an additional ferromagneticlayer such that a free layer is formed from dual SAF. FIG. 3 is aconceptual block diagram of a layer stack 30 that includes a compositefree layer with a dual synthetic antiferromagnetic structure, inaccordance with examples of the disclosure. Layer stack 30 includes aseed layer/first electrode 32, a first ferromagnetic layer 34 on seedlayer/first electrode 32, a first non-magnetic layer (as a spacer) 36 onfirst ferromagnetic layer 34, a second ferromagnetic layer 38 on firstnon-magnetic layer 36, a second non-magnetic layer (as a spacer) 40 onsecond ferromagnetic layer 38, a third ferromagnetic layer 42 on secondnon-magnetic layer 40, a dielectric barrier layer 44 on thirdferromagnetic layer 42, and a cap layer/second electrode 44 on thirdferromagnetic layer 42. Seed layer/first electrode 32, firstferromagnetic layer 34, dielectric barrier layer 44, and caplayer/second electrode 46 may be similar to or substantially the same asseed layer/first electrode 12, first ferromagnetic layer 14, dielectricbarrier layer 20, and cap layer/second electrode 22 of layer stack 10 ofFIG. 1.

First non-magnetic layer 36 and second non-magnetic layer 40 may besimilar to or substantially the same as non-magnetic layer 16 of layerstack 10 of FIG. 1. First non-magnetic layer 36 and second non-magneticlayer 40 may be the same or different. For example, first non-magneticlayer 36 and second non-magnetic layer 40 may be formed of the same ordifferent materials, and may define the same or different thicknesses.The compositions and thicknesses of first non-magnetic layer 36 andsecond non-magnetic layer 40 may be selected to achieve a desired typeand strength of magnetic coupling between first ferromagnetic layer 34and second ferromagnetic layer 38 and between second ferromagnetic layer38 and third ferromagnetic layer 42, respectively. For example, athickness of first non-magnetic layer 36 and a thickness of secondnon-magnetic layer 40 may be selected so that first ferromagnetic layer34 and second ferromagnetic layer 38 are antiferromagnetically coupledin the absence of a bias voltage and second ferromagnetic layer 38 andthird ferromagnetic layer 42 are also antiferromagnetically coupled inthe absence of a bias voltage. In some examples, a thickness of secondnon-magnetic layer 40 may be selected so that the IEC between secondferromagnetic layer 38 and third ferromagnetic layer 42 is less inmagnitude than the IEC between first ferromagnetic layer 34 and secondferromagnetic layer 38. This may result in magnetization of thirdferromagnetic layer 42 switching at a lower bias voltage thanmagnetization of second ferromagnetic layer 38 and first ferromagneticlayer 34. Thus, by selection of an appropriate bias voltage (e.g.,greater than a voltage that causes magnetization of third ferromagneticlayer 42 to switch and less than a voltage that causes magnetizations ofsecond ferromagnetic layer 38 and first ferromagnetic layer 34 toswitch) can be used to switch magnetic orientation of thirdferromagnetic layer 42.

Second ferromagnetic layer 38 may be similar to or substantially thesame as first ferromagnetic layer 14 of layer stack 10 in FIG. 1. Firstferromagnetic layer 34 and second ferromagnetic layer 38 may be the sameor different. For example, first non-magnetic layer 36 and secondnon-magnetic layer 40 may be formed of the same or different materials,and may define the same or different thicknesses. The compositions andthicknesses of first ferromagnetic layer 34 and second ferromagneticlayer 38 may be selected to achieve a desired type and strength ofmagnetic coupling between first ferromagnetic layer 34 and secondferromagnetic layer 38. For example, compositions and thicknesses offirst ferromagnetic layer 34 and second ferromagnetic layer 38 may beselected to achieve relatively strong antiferromagnetic IEC betweenfirst ferromagnetic layer 34 and second ferromagnetic layer 38 so thatmagnetic orientations of first ferromagnetic layer 34 and secondferromagnetic layer 38 do not switch under the influence of the biasvoltages applied by voltage source 46. In this way, first ferromagneticlayer 34, first non-magnetic layer 36, and second ferromagnetic layer 38may form a relatively stable synthetic antiferromagnet (SAF) structurein which the IEC (J₁) is negative.

Third ferromagnetic layer 42 may include compositions similar to secondferromagnetic layer 18 of layer stack 10 of FIG. 1. For example, thirdferromagnetic layer 42 may include a CoFeB alloy, such as Co₂₀Fe₆₀B₂₀; aCoFe alloy, Co, Fe, a Co-based Heusler alloy, or a Mn-based Heusleralloy. Third ferromagnetic layer 42 may define any suitable thickness,such as between about 0.5 nm and about 10 nm, such as between about 1 nmand about 4 nm, or about 2 nm. In some examples, third ferromagneticlayer 42 includes a CoFeB alloy and a thickness of about 1.3 nm.

The composition and thickness of third ferromagnetic layer 42 may beselected to achieve a desired type and strength of magnetic couplingbetween second ferromagnetic layer 38 and third ferromagnetic layer 42.For example, compositions and thicknesses of second ferromagnetic layer38 and third ferromagnetic layer 42 may be selected to achieverelatively weaker antiferromagnetic IEC between second ferromagneticlayer 38 and third ferromagnetic layer 42 than between firstferromagnetic layer 34 and second ferromagnetic layer 38 so that themagnetic orientation of third ferromagnetic layer 42 switches under theinfluence of the bias voltages applied by voltage source 46. In thisway, second ferromagnetic layer 38, second non-magnetic layer 40, andthird ferromagnetic layer 42 may form a relatively less stable syntheticantiferromagnet (SAF) structure in which the IEC (J₁) is negative in theabsence of a bias voltage.

Upon application of a bias voltage may tune the magnetic anisotropy ofthird ferromagnetic layer 42 and magnetic coupling between secondferromagnetic layer 38 and third ferromagnetic layer 42 fromantiferromagnetic (IEC between second ferromagnetic layer 38 and thirdferromagnetic layer 42, J₂, is less than 0) and ferromagnetic (IECbetween second ferromagnetic layer 38 and third ferromagnetic layer 42,J₂, is greater than 0). This may be similar to operation of layer stack10 of FIG. 1 as shown in FIGS. 2A and 2B, aside from the presence of thestable SAF formed by first ferromagnetic layer 34, first non-magneticlayer 36, and second ferromagnetic layer 38.

Due to the bidirectional switching of the perpendicular composite freelayers with SAF structures shown in FIGS. 1 and 3, the perpendicularcomposite free layers may be incorporated in perpendicular magnetictunnel junctions (p-MTJs). FIG. 4 is a conceptual block diagram of anexample p-MTJ 50 that includes a synthetic antiferromagnet free layer,in accordance with examples of the disclosure. Like layer stack 10 ofFIG. 1, p-MTJ 50 of FIG. 4 includes a seed layer/first electrode 52, afirst ferromagnetic layer 54 on seed layer/first electrode 52, anon-magnetic layer 56 on first ferromagnetic layer 54, and a secondferromagnetic layer 58 on non-magnetic layer 56. Seed layer/firstelectrode 52, first ferromagnetic layer 54, non-magnetic layer 56, andsecond ferromagnetic layer 58 may be similar to or substantially thesame as seed layer/first electrode 12, first ferromagnetic layer 14,non-magnetic layer 16, and second ferromagnetic layer 18 of layer stack10 of FIG. 1. Together, first ferromagnetic layer 54, non-magnetic layer56, and second ferromagnetic layer 58 form a synthetic antiferromagnet(SAF) free layer 60.

Unlike layer stack 10 of FIG. 1, p-MTJ 50 of FIG. 4 includes a tunnelbarrier layer 62 on second ferromagnetic layer 58 and a reference layer64 on tunnel barrier layer 62. Tunnel barrier layer 62 may include anelectrically insulating material, such as MgO, AlO_(x), or MgAlO_(x),though which electrons must tunnel to conduct charge from SAF free layer60 to reference layer 64. Tunnel barrier layer 62 may define a thicknesson the order of single digit nanometers, such as between about 1 nm andabout 2.5 nm, or about 2 nm.

Reference layer 64 includes a ferromagnetic or ferrimagnetic materialwhose magnetic moment is substantially fixed for electric fields, biasvoltages, magnetic fields, spin transfer torque (STT), or spin orbittorque (SOT) to which reference layer 64 is exposed during operation ofp-MTJ 50. Reference layer 64 may include any suitable ferromagnetic orferrimagnetic material. In some examples, may include, for example, aCoFeB alloy, such as Co₂₀Fe₆₀B₂₀; a CoFe alloy, Co, Fe, a Co-basedHeusler alloy, or a Mn-based Heusler alloy, FePd, FePt, FePdPt, Co—Pd,Co—Pt, CoPdPt, FeNiPd, FeNiPt, MnAl, or the like. Reference layer 64 maydefine any suitable thickness, such as between about 1 nm and about 12nm, such as between about 1 nm and about 4 nm, or about 2 nm, or betweenabout 3 nm and about 12 nm. In some examples, reference layer 64includes a CoFeB alloy and a thickness of about 1.3 nm. In someexamples, reference layer 64 may include multiple layers, such as aferromagnetic or ferrimagnetic layer antiferromagnetically coupled to anantiferromagnetic layer.

P-MTJ 50 also includes a cap layer/second electrode 66, which may besimilar to or substantially the same as cap layer/second electrode 22 oflayer stack 10 of FIG. 1.

During operation of p-MTJ 50, a write controller may control voltagesource 68 to apply a bias voltage of a selected sign and magnitudeacross p-MTJ 50. As described above with reference to FIG. 1, the biasvoltage may affect magnetic anisotropy of second ferromagnetic layer anda sign of IEC associated with spacer layer 56. Thus, the bias voltagemay cause switching of magnetic orientation of second ferromagneticlayer 58. The magnetic orientation of second ferromagnetic layer 58affects the resistance of p-MTJ 50, which may be read by conducting acurrent from current source 70 through p-MTJ 50.

In some examples, a p-MTJ may include the layer stack 30 shown in FIG.3. For example, FIG. 5 is a conceptual block diagram of a p-MTJ 80 thatincludes a dual SAF free layer 94, in accordance with examples of thedisclosure. Like layer stack 30 of FIG. 3, p-MTJ 80 of FIG. 5 includes aseed layer/first electrode 82, a first ferromagnetic layer 84 on seedlayer/first electrode 82, a first spacer layer 86 on first ferromagneticlayer 84, a second ferromagnetic layer 88 on first non-magnetic layer86, a second non-magnetic layer 90 on second ferromagnetic layer 88, anda third ferromagnetic layer 92 on second non-magnetic layer 90. Seedlayer/first electrode 82, first ferromagnetic layer 84, firstnon-magnetic layer 86, second ferromagnetic layer 88, secondnon-magnetic layer 90, and third ferromagnetic layer 90 may be similarto or substantially the same as seed layer/first electrode 32, firstferromagnetic layer 34, first non-magnetic layer 36, secondferromagnetic layer 38, second non-magnetic layer 40, and thirdferromagnetic layer 42 of layer stack 30 of FIG. 3. Together, firstferromagnetic layer 84, first non-magnetic layer 86, secondferromagnetic layer 88, second non-magnetic layer 90, and thirdferromagnetic layer 92 form a dual SAF free layer 94.

Unlike layer stack 30 of FIG. 3, p-MTJ 80 of FIG. 5 includes a tunnelbarrier layer 96 on third ferromagnetic layer 92 and a reference layer98 on tunnel barrier layer 96. Tunnel barrier layer 96 and referencelayer 98 may be similar to or substantially the same as tunnel barrierlayer 62 and reference layer 64 of p-MTJ 50 of FIG. 4. P-MTJ 80 alsoincludes a cap layer/second electrode 100, which may be similar to orsubstantially the same as cap layer/second electrode 46 of layer stack30 of FIG. 3.

FIGS. 6A and 6B are conceptual diagrams illustrating examples of p-MTJ80 of FIG. 5 under a positive bias voltage from voltage source 102 and anegative bias voltage from voltage source 102, respectively. As shown inFIG. 6A, first ferromagnetic layer 84 may have a magnetic orientation inthe positive z-axis direction of FIG. 6A and second ferromagnetic layer88 may have a magnetic orientation in the negative z-axis direction ofFIG. 6A. First non-magnetic layer 86 has a negative IEC energy (J₁<0),indicating that first ferromagnetic layer 84 and second ferromagneticlayer 88 are antiferromagnetically coupled.

The positive bias voltage causes accumulation of electrons from theinterface of third ferromagnetic layer 92 and tunnel barrier layer 96,as shown by the negative charges accumulated at the interface. Theaccumulation of electrons at the interface of third ferromagnetic layer92 and tunnel barrier layer 96 causes a reduction in the minority spindensity (d orbitals) and second ferromagnetic layer 88 and thirdferromagnetic layer 92 are ferromagnetically coupled. Further, the IEC(J₁) is positive, making the ferromagnetic coupling the energeticallystable state.

As shown in FIG. 6B, when a negative bias voltage is applied by voltagesource 102 to seedlayer/first electrode 82, electrons deplete at theinterface of third ferromagnetic layer 92 and tunnel barrier layer 96.The depletion of electrons at the interface enhances the minority spindensity (d orbitals) and second ferromagnetic layer 88 and secondferromagnetic layer 92 are anti-ferromagnetically coupled. Further, theIEC (J₁) is negative, making the anti-ferromagnetic coupling theenergetically stable state.

In some examples, the top reference layer (e.g., reference layer 98)induces a large stray field, which may reduce the thermal stability andincrease J_(c) of the p-MTJ, such as p-MTJ 50 or 80. This may beaddressed by using a SAF reference layer, which can significantly reduceJ_(c) and enhance thermal stability. FIG. 7 is a conceptual blockdiagram of a p-MTJ that includes a dual SAF free layer and a SARreference layer, in accordance with examples of the disclosure. LikeP-MTJ 80 of FIG. 5, p-MTJ 110 of FIG. 7 includes a seed layer/firstelectrode 112, a first ferromagnetic layer 114 on seed layer/firstelectrode 112, a first spacer layer 116 on first ferromagnetic layer114, a second ferromagnetic layer 118 on first non-magnetic layer 116, asecond non-magnetic layer 120 on second ferromagnetic layer 118, and athird ferromagnetic layer 122 on second non-magnetic layer 120, and atunnel barrier layer 126 on third ferromagnetic layer 122. Together,first ferromagnetic layer 114, first non-magnetic layer 116, secondferromagnetic layer 118, second non-magnetic layer 120, and thirdferromagnetic layer 122 form a dual SAF free layer 124. Seed layer/firstelectrode 112, first ferromagnetic layer 114, first non-magnetic layer116, second ferromagnetic layer 118, second non-magnetic layer 120,third ferromagnetic layer 122, and tunnel barrier layer 126 may besimilar to or substantially the same as seed layer/first electrode 82,first ferromagnetic layer 84, first non-magnetic layer 86, secondferromagnetic layer 88, second non-magnetic layer 90, thirdferromagnetic layer 92, and tunnel barrier layer 96 of p-MTJ 80 of FIG.5.

Unlike p-MTJ 80 of FIG. 5, p-MTJ 110 of FIG. 7 includes a SAF referencelayer 134, which includes a fourth ferromagnetic layer 128, a thirdnon-magnetic layer 130 on fourth ferromagnetic layer 128, and a fifthferromagnetic layer 132 on third non-magnetic layer 130. Fourthferromagnetic layer 128 may be similar to or substantially the same asthird ferromagnetic layer 122, third non-magnetic layer 130 may besimilar to or substantially the same as first non-magnetic layer 116 orsecond non-magnetic layer 120, and fifth ferromagnetic layer 132 may besimilar to or substantially the same as first ferromagnetic layer 114 orsecond ferromagnetic layer 118. Fourth ferromagnetic layer 128 isantiferromagnetically coupled to fifth ferromagnetic layer 132. Theantiferromagnetic coupling may be designed to be sufficiently strongthat a magnetic orientation of SAF reference layer 134 does not changefor electric fields, bias voltages, magnetic fields, spin transfertorque (STT), or spin orbit torque (SOT) to which SAF reference layer134 is exposed during operation of p-MTJ 110. A SAF reference layer 134may generate a smaller stray field than a reference layer that includesa single ferromagnetic or ferrimagnetic layer.

In some examples, the layer stacks or MTJs described herein may be usedas spin memory or logic devices. For example, the layer stacks or MTJsdescribed herein may be used as spin memory or logic devices formagnetoresistive random access memory.

In some examples, the layer stacks or MTJs described herein may be usedas random bit stream generators. For example, the layer stacks or MTJsdescribed herein may be used as random bit stream generators forstochastic computing devices or stochastic spiking neural networkdevices. FIG. 17 is a conceptual diagram of a stochastic numbergenerator configured to generate a stochastic bit stream. The stochasticnumber generator includes a random number generator and a constantnumber register. The outputs of the random number generator and theconstant number register are input to a comparator, which outputs astochastic bit stream. The layer stacks or MTJs described herein may beused as the random number generator in the stochastic number generatorof FIG. 17.

EXAMPLES

To demonstrate E-field switching of p-MTJs with a composite SAF freelayer, a FePd SAF p-MTJ stack was fabricated. The p-MTJ stack wasprepared on single crystalline (001) MgO substrate using a magnetronsputtering system under ultra-high vacuum (base pressure <5.0×10⁻⁸Torr). The metal layers were deposited by DC sputtering and the MgOtunnel barrier layer was deposited by RF sputtering. The p-MTJ stack hadthe configuration shown in FIG. 8A. A 15 nm layer of Cr was deposited onthe MgO substrate and a 5 nm layer of Pt was deposited on the 15 nmlayer of Cr to form a seed structured. The seed structure was depositedwhile the MgO substrate was maintained at a temperature of about 350° C.

A 3 nm layer of FePd was deposited on the 5 nm layer of Pt, a 1.1 nmlayer of Ru was deposited on the 3 nm layer of FePd, and a 3 nm layer ofFePd was deposited on the 1.1 nm layer of Ru. Together, the 3 nm layerof FePd/1.1 nm layer of Ru/3 nm layer of FePd formed a perpendicularsynthetic antiferromagnetic stack. The layers of the syntheticantiferromagnetic stack were deposited while the MgO substrate wasmaintained at a temperature of about 350° C.

The remaining layers were deposited after the MgO substrate cooled toroom temperature. A 0.8 nm layer of Ta was deposited on the 3 nm layerof FePd and a 1.3 nm layer of Co₂₀Fe₆₀B₂₀ was deposited on the 0.8 nmlayer of Ta. Together, the 3 nm layer of FePd/1.1 nm layer of Ru/3 nmlayer of FePd/0.8 nm layer of Ta/1.3 nm layer of Co₂₀Fe₆₀B₂₀ formed adual SAF free layer. A tunnel barrier layer of 2 nm of MgO was depositedon the 1.3 nm layer of Co₂₀Fe₆₀B₂₀. A reference layer was then formed onthe tunnel barrier layer. The reference layer included a 1.3 nm layer ofCo₂₀Fe₆₀B₂₀ on the tunnel barrier layer, a non-magnetic layer of 0.7 nmTa on the 1.3 nm layer of Co₂₀Fe₆₀B₂₀, and a multilayer stack including5 pairs of [0.7 nm Pd/0.3 nm Co] on the 0.7 nm layer of Ta. A 5 nm layerof Ta as a capping layer was on the multilayer stack.

The capping layer depended on the tests to which the p-MTJ was to besubjected. For p-MTJs to be tested using four-probe tests, a cappinglayer of 5 nm Ta was used, as shown in FIG. 8A. For p-MTJs to be testedusing conductive atomic force microscopy (C-AFM), the capping layer was15 nm of Pt.

Before device patterning, the p-MTJs were annealed at 350° C. and 400°C. using rapid thermal annealer. The p-MTJs were patterned intonano-pillars using e-beam lithography and Ar ion milling. Electricalcontacts were formed on the capping layer from a 10 nm layer of Ti and a120 nm layer of Au on the 10 nm layer of Ti. The spin transportproperties were tested by four-probe technique for 150-nm and 500-nmdiameter p-MTJs using a Dynacool PPMS at different temperatures. Spintransport properties were tested for 35-100 nm diameter FePd SAF p-MTJsusing a C-AFM setup at room temperature.

The C-AFM equipment was an RHK UHV350 with R9 controller operating incontact mode. Si-doped AFM probe tips from Arrow-FM nanoworld were madeconductive by sputtering a layer of Pt with a 200 nm nominal thicknesson a Ta adhesion layer. A sharp AFM tip with 20 nm of conductive Ptcoated was used to make electrical contact directly with the top of FePdSAF p-MTJ pillars. In all the measurements, the tip was grounded and thebias voltage (positive or negative) was applied at the bottom seedlayer. Thus, for a positive bias voltage (V_(bias)), the current flowedfrom the bottom to the top of the p-MTJ stack, and for a negativeV_(bias), the current flowed from the top to the bottom of p-MTJ stack.

During the testing, a sweep rate of 150 Oe/sec was used to measure theresistance versus magnetic field (R-H) loops. A sweep rate of 500 mV/secwas used to measure the resistance versus bias voltage (R-V) loops. Forresistance versus time (R-t) traces, an acquisition rate of 1 MHz wasused. A variable out-of-plane magnetic field H_(ext) up to 1300 Oe wasapplied by an electromagnet directly below the sample stage.

In the bottom dual SAF free layer of FIG. 8A, two L1₀-FePd layers areantiferromagnetically coupled through a Ru non-magnetic spacer layer.The magnetic anisotropy and interlayer exchange coupling strength(J_(IEC)) of the FePd/Ru/FePd p-SAF structure were calculated to beabout 1.0×10⁷ erg/cm³ and about −2.60 erg/cm², respectively. As shown inFIG. 8A, the FePd/Ru/FePd p-SAF structure then couples with a CoFeBlayer through a Ta layer, which also exhibits AFM coupling. Besidesfunctioning as a spacer layer, the Ta layer also enhances the i-PMA ofthe CoFeB ferromagnetic layer with the MgO tunnel barrier layer.

FIG. 8B is a plot of an out-of-plane magnetic hysteresis (M-H) loop of adual p-SAF free layer with a stack of FePd(3 nm)/Ru(1.1 nm)/FePd(3nm)/Ta(0.8 nm)/CoFeB(1.3 nm). The plot of FIG. 8B was generated afterannealing the layers at 350° C. The inset of FIG. 8B shows the minor M-Hloop of the dual p-SAF structure, where anti-ferromagnetic coupling wasobserved between FePd and CoFeB layers. As shown in FIG. 8B, goodanti-ferromagnetic coupling was observed among the three ferromagneticlayers (FePd, FePd, and CoFeB). This is further illustrated in FIG. 9,which shows the out-of-plane magnetic hysteresis (M-H) loop of a FePdp-SAF free layer with a stack of FePd(3 nm)/Ru(1.1 nm)/FePd(3 nm). FIG.9 shows that spin-flop switching and spin-flip switching are observed ata high and low applied magnetic field, respectively. The FePd/Ru/FePdp-SAF shows the strongest interlayer exchange coupling property with astrength J_(IEC) of about −2.60 erg/cm². The FePd/Ta/CoFeB structureshows comparatively weak AFM coupling with an obvious two-stepswitching, as shown in the inset of FIG. 8B.

Subsequently, the p-MTJ stacks shown in FIG. 8A were patterned into150-nm diameter p-MTJ pillars using e-beam lithography and Ar ionmilling. FIG. 8C is a microscopy image of the 150-nm diameter p-MTJpillar. The spin-transport properties (magnetoresistance versus externalmagnetic field, MR-H) of FePd SAF p-MTJs annealed at 350° C. weremeasured by a standard four-probe resistance measurement technique byusing a Dynacool physical properties measurement system (PPMS). FIG. 10is a plot of normalized magnetoresistance versus applied field forp-MTJs with 150 nm and 500 nm diameter and SAF free layers at roomtemperature. As shown in FIG. 10, the switching field (H_(swf)) of thedual p-SAF free layer increased from about 390 Oe to about 700 Oe whenthe diameter of p-MTJ pillar was decreased from about 500 nm to about150 nm.

FIG. 8D is a plot illustrating magnetoresistance-applied field loops asa function of temperature for p-MTJs with 150 nm diameter and SAF freelayers. The magnetoresistance-applied field loops were obtained at 5 K(loop 160), 100 k (loop 162), and 300 K (loop 164). Each of the loops160, 162, 164 exhibited a plateau in the high-resistance state and sharpmagnetization switching between the parallel and anti-parallel stateswhile sweeping the applied perpendicular external magnetic field(H_(ext)), implying that both the free and reference layer structurespossess good perpendicular magnetic anisotropy. The magnetoresistanceratio is calculated to be about 8.0% at 300 K and about 16.0% at 5 K. Aresistance-area (RA) product of about 30 kΩ*μm² is obtained with a2-nm-thick MgO tunnel barrier.

To quantitatively evaluate the E-field effect for the dual p-SAF freelayer of p-MTJs, the mean H_(swf), magnetic anisotropy (K_(u,eff)), andcoefficiency (ξ) of the voltage-controlled magnetic anisotropy (VCMA) ofthe dual p-SAF free layer were obtained by measuring minor M-H loops andfitting the switching field distribution (SFD). The 350° C.-annealedFePd SAF p-TMJ stacks were patterned into sub-100 nm diameter MTJpillars by using an e-beam lithography and Ar ion etching. FIGS. 11A-11Cillustrate a scanning electron microscopy (SEM) image of a top view ofthe 350° C.-annealed FePd SAF p-TMJ stacks with diameters ranging fromabout 35 nm to about 250 nm, an atomic force microscopy (AFM) imageillustrating topography of the pillars, and a current map measured byconductive AFM at 100 mV, respectively.

The minor MR-H loop of the sub-100 nm FePd SAF p-MTJ devices wasmeasured using a conductive atomic force microscope (C-AFM) by sweepinga perpendicular external magnetic field (H_(ext)). FIG. 12A is aconceptual and schematic diagram illustrating the experimental setup, inwhich the AFM tip is grounded and the bias voltage (V_(bias)) is appliedat the MgO substrate. FIG. 12B is a plot of minor magnetoresistanceversus applied perpendicular external magnetic field (H_(ext)) for100-nm diameter FePd SAF p-MTJs at different bias voltages(V_(bias)=+0.75 V, −0.1 V and −0.75 V, respectively). In the example ofFIG. 12B, the positive bias voltage enhances the switching field(H_(swf)) and the negative bias voltage reduces the switching field(H_(swf)). This indicates that the applied electric field affects themagnetic anisotropy of the bottom dual SAF free layer. Due to the strayfield (dipole coupling) from the top reference layer, the shift of theminor MR-H loop was observed.

To evaluate the switching field distribution (SFD), multiplemagnetoresistance versus applied perpendicular external magnetic field(H_(ext)) loops were measured at a given V_(bias). The mean coercivity(H_(c)) value was obtained by fitting SFD using theKurkijarvi-Fulton-Dunkelberger equation:

$\sigma = \left\{ {\frac{1}{\tau_{0}v}{\exp\left\lbrack {{- K_{eff}}{V\left( {1 - \left( \frac{{HM}_{s}}{2K_{eff}} \right)^{2}} \right\rbrack}} \right\}} \times \exp \left\{ {- {\int\limits_{0}^{H}{\frac{1}{\tau_{0}v}{\exp\left\lbrack {\frac{{- K_{eff}}V}{k_{b}T}\left( {1 - \frac{{hM}_{s}}{2K_{eff}}} \right)^{2}} \right\rbrack}{dh}}}} \right\}} \right.$

Where τ₀ is the attempt time (equal to 10⁻⁹ s), v is the ramping rate ofH_(ext) (equal to about 350 Oe/s), Ms is the saturation magnetization ofthe bottom dual SAF free layer (equal to about 970 emu/cm³), k_(B) isthe Boltzmann constant, and T is the testing temperature (equal to 300K). FIG. 12C is a plot depicting the mean coercivity (H_(c)) of thebottom dual SAF free layer as a function of the bias voltage (V_(bias)).The mean coercivity of the bottom dual SAF free layer shows a typicallylinear behavior, which presents the same trend with the theoreticalcalculation and experimental results. The mean coercivity valuedramatically increases from about 145 Oe to about 900 Oe when the biasvoltage (V_(bias)) increases from from −0.75 V to +0.75 V.

This increasing mean coercivity value is more than one order magnitudelarger than that of p-MTJs with a CoFeB single layer. FIG. 13 is a plotdepicting the mean coercivity (H_(c)) of the bottom dual SAF free layeras a function of the bias voltage (V_(bias)) in comparison to meancoercivity (H_(c)) of a CoFeB/MgO/CoFeB p-MTJ as a function of biasvoltage. For FePd SAF p-MTJs, the mean coercivity (H_(c)) shows adramatic increase from 145 Oe to 900 Oe as the bias voltage increasesfrom −0.75 volts to 0.75 volts. However, the mean coercivity (H_(c))only increases from 205 Oe to 290 Oe for the CoFeB p-MTJs. The largermean coercivity is believed to be due to the electric field from thebias voltage modifying the magnetic anisotropy of the ferromagneticlayer(s), further enhancing or reducing the strength of the couplingbetween ferromagnetic layers, which results in the significant change ofthe mean coercivity (H_(c)) value.

In this example, the positive bias voltage increases the i-PMA of theTa/CoFeB/MgO stack in the FePD dual SAF p-MTJ, which enhances the AFMcoupling between the CoFeB and FePd layers, showing the increasing ofthe H_(c) of the bottom dual SAF free layer. In contrast, the negativebias voltage decreases the i-PMA of the CoFeB layer, which leads toferromagnetic coupling between the CoFeB and FePd layers and decreasesthe H_(c) of the bottom dual SAF free layer.

K_(u,eff) was then calculated and ξ evaluated for the bottom dual SAFfree layer at the different bias voltages (V_(bias)) by fitting SFDusing the equation presented above. FIG. 12D is a plot of K_(u,eff)versus bias voltage. When the bias voltage (V_(bias)) changes from −0.75V to +0.75 V, K_(u,eff) linearly increases from 0.15 Merg/cm³ to 0.53Merg/cm³. The value is calculated by following the equation of

${{K_{eff}\left( V_{bias} \right)} = {{K_{eff}(0)} - \frac{\xi \; V_{bias}}{t_{MgO}^{2}}}},$

where K_(eff)(0) is about 0.395 Merg/cm³ and is the magnetic anisotropyof the bottom dual SAF free layer with V_(bias)=0, and t_(MgO) is theMgO thickness. By fitting the K_(u,eff) curve, the of the bottom dualSAF free layer was evaluated to be about 117 fJ/(V*m).

The feasibility of electric field switching of the p-MTJ devices wasthen investigated. The current versus bias voltage (V_(bias)) curve ofthe sub-100 nm FePd SAF p-MTJ devices was measured at room temperatureusing the same C-AFM setup without applying the perpendicular externalmagnetic field (H_(ext)). The I-V curves were obtained by sweepingV_(bias) from −0.6 V to +0.6 V for 100-nm diameter FePd SAF p-MTJdevices annealed at 350° C. FIG. 14A is a plot of the I-V curve. Sharpmagnetization switching is clearly seen in the insets of FIG. 14A when anegative bias voltage of about −0.46 V (I=−8.92 μA) and a positive biasvoltage of about +0.48 V (I=+8.73 μA) were applied, respectively. Thisindicates that the magnetization is switched from the parallel state tothe antiparallel state and then switched back from the antiparallelstate to the parallel state. The magnetoresistance ratios werecalculated to be about 6.9% and about 3.7% and the switching currentdensities (J_(c)) were evaluated to be about 1.13×10⁵ A/cm² and about1.11×10⁵ A/cm² for the parallel to antiparallel state change andantiparallel to parallel state change, respectively.

To further confirm the electric-field driven bi-directionalmagnetization switching in p-MTJs, the current vs. time curve wasmeasured while applying a voltage pulse for 100-nm diameter FePd SAFp-MTJs, as presented in FIG. 14B. FIG. 14B illustrates plots of biasvoltage versus time and current versus time for 100-nm diameter FePd SAFp-MTJs. During the measurement, negative and positive 0.85 V pulses wereapplied for writing, then a positive 0.1 V pulse was used to read theresistance. As shown in FIG. 14B, the p-MTJ has a low resistance valueat the initial, parallel state. Writing with a positive +0.85 V voltagepulse induces the antiparallel state and a relatively higher resistanceis obtained. Writing with a negative −0.85 V voltage pulse induces theparallel state exhibiting a relatively lower resistance. Because of thelarge RA and a low switching current density ˜1.1×10⁵ A/cm², thereshould have been a very limited spin-transfer torque (STT) effect.

The switching was also observed in 35-nm diameter FePd SAF p-MTJsannealed at 400° C., as shown in FIG. 15. FIG. 15 is a plot of a currentversus bias voltage (V_(bias)) curve (I-V curve) obtained by sweepingthe bias voltage (V_(bias)) from −2.1 V to +2.1 V for a 35-nm diameterFePd SAF p-MTJ devices annealed at 400° C. Annealing at 400° C.satisfies the requirement of the temperatures used for back-end-of-lineprocesses for existing complementary metal-oxide-semiconductor (CMOS)technologies. The magnetization is switched from parallel toantiparallel and antiparallel to parallel states with a negative(V_(bias)) of about −2.06 V (1=8.8 μA) and a positive bias voltage(V_(bias)) of about +1.8 V (1=5.7 μA), respectively. The correspondingmagnetoresistance ratios are about 5.5% for the antiparallel to parallelstate change with J_(c) equal to about 1.4×10⁵ A/cm² and about 5.7% forthe parallel to antiparallel state with J_(c) equal to about 2.2×10⁵A/cm².

A 40-nm diameter p-MTJ device annealed at 350° C. showed the uniqueproperty of the bias voltage-controlled random magnetization switching.FIG. 16 is a plot of a current versus bias voltage (V_(bias)) curve (I-Vcurve) obtained by sweeping the bias voltage (V_(bias)) from −1.5 V to+1.7 V for a 40-nm diameter FePd SAF p-MTJ devices annealed at 350° C.Telegraphic magnetization switching was observed when sweeping the biasvoltage (V_(bias)) from +1.55 V to +1.28 V. As the bias voltage(V_(bias)) continues to decrease, the telegraphic switching disappears.A single parallel to antiparallel state magnetization switching wasobserved with the bias voltage (V_(bias)) equal to about −0.92 V. Thesecharacteristics of p-MTJs obtained could be used to realize stochasticcomputing devices and stochastic spiking neural networks.

Various examples have been described. These and other examples arewithin the scope of the following claims.

What is claimed is:
 1. A magnetic device comprising: a layer stackcomprising: a first ferromagnetic layer; a non-magnetic spacer layer onthe first ferromagnetic layer, wherein the non-magnetic spacer layercomprises at least one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr, or V; asecond ferromagnetic layer on the non-magnetic spacer layer; an oxidelayer on the second ferromagnetic layer; a voltage source configured toapply a bias voltage across the layer stack to cause switching of amagnetic orientation of the second ferromagnetic layer withoutapplication of an external magnetic field or a current, wherein athickness and composition of the non-magnetic spacer layer is selectedto enable a switching direction of the magnetic orientation of thesecond ferromagnetic layer to be controlled by a sign of the biasvoltage.
 2. The magnetic device of claim 1, wherein a thickness ofnon-magnetic spacer layer is selected to cause antiferromagneticcoupling of the first ferromagnetic layer and the second ferromagneticlayer in the absence of the bias voltage.
 3. The magnetic device ofclaim 1, wherein: the first ferromagnetic layer comprises at least oneof a FePd alloy, a FePt alloy, a CoPd alloy, a CoPt alloy, a MnAl alloy,a MnBi alloy, a MnGaN alloy, a MnGeN alloy, or a Mn-based Heusler alloy;and the second ferromagnetic layer comprises at least one of a CoFeBalloy, a CoFe alloy, a Co-based alloy, a Fe-based alloy, a Co-basedHeusler alloy, or a Mn-based Heusler alloy.
 4. The magnetic device ofclaim 1, wherein a sign of the bias voltage affects a sign or strengthof the interlayer exchange coupling between the first ferromagneticlayer and the second ferromagnetic layer.
 5. The magnetic device ofclaim 1, further comprising: a second non-magnetic layer comprising atleast one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr or V; and a thirdferromagnetic layer, wherein: the first ferromagnetic layer is on thesecond non-magnetic layer and the second non-magnetic layer is on thethird ferromagnetic layer; a thickness and a composition of the secondnon-magnetic layer are selected such that the third ferromagnetic layerand the second ferromagnetic layer are antiferromagnetically coupled;and the thickness and the composition of the second non-magnetic layerand a thickness and a composition of the non-magnetic layer are selectedso that interlayer exchange coupling between the second ferromagneticlayer and the third ferromagnetic layer is stronger than interlayerexchange coupling between the first ferromagnetic layer and the secondferromagnetic layer.
 6. The magnetic device of claim 1, wherein theoxide layer is a tunnel barrier layer comprising MgO, further comprisinga reference ferromagnetic layer on the tunnel barrier layer, wherein themagnetic device is a magnetic tunnel junction.
 7. The magnetic device ofclaim 6, wherein the reference ferromagnetic layer comprises a syntheticantiferromagnet.
 8. The magnetic device of claim 1, further comprising awrite controller configured to control the voltage source to output aselected bias voltage.
 9. The magnetic device of claim 8, wherein thewrite controller is configured to control the voltage source to output abias voltage configured to enable stable bi-directional or randomtelegraphic switching of the magnetic orientation of the secondferromagnetic layer at room temperature.
 10. A method comprising:controlling, by a write controller, a voltage source to output apositive bias voltage across a layer stack, wherein the layer stackcomprises: a first ferromagnetic layer; a non-magnetic spacer layer onthe first ferromagnetic layer, wherein the non-magnetic spacer layercomprises at least one of Ru, Ir, Ta, Cr, W, Mo, Re, Hf, Zr or V; asecond ferromagnetic layer on the non-magnetic spacer layer; an oxidelayer on the second ferromagnetic layer, wherein the positive biasvoltage causes switching of a magnetic orientation of the secondferromagnetic layer from a first direction to a second direction withoutapplication of an external magnetic field or a current; and controlling,by the write controller, the voltage source to output a negative biasvoltage across the layer stack, wherein the negative bias voltage causesswitching of the magnetic orientation of the second ferromagnetic layerfrom the second direction to the first direction without application ofan external magnetic field or a current.
 11. The method of claim 10,wherein a thickness of non-magnetic spacer layer is selected to causeantiferromagnetic coupling of the first ferromagnetic layer and thesecond ferromagnetic layer in the absence of the bias voltage.
 12. Themethod of claim 10, wherein: the first ferromagnetic layer comprises atleast one of a FePd alloy, a FePt alloy, a CoPd alloy, a CoPt alloy, aMnAl alloy, a MnBi alloy, a MnGaN alloy, a MnGeN alloy, or a Mn-basedHeusler alloy; and the second ferromagnetic layer comprises at least oneof a CoFeB alloy, a CoFe alloy, a Co-based alloy, a Fe-based alloy, aCo-based Heusler alloy, or a Mn-based Heusler alloy.
 13. The method ofclaim 10, wherein a sign of the bias voltage affects a sign or strengthof the interlayer exchange coupling between the first ferromagneticlayer and the second ferromagnetic layer.
 14. The method of claim 10,wherein the layer stack further comprises: a second non-magnetic layercomprising at least one of Ru, Ir, Ta, Cr, W, Mo, or V; and a thirdferromagnetic layer, wherein: the first ferromagnetic layer is on thesecond non-magnetic layer and the second non-magnetic layer is on thethird ferromagnetic layer; a thickness and a composition of the secondnon-magnetic layer are selected such that the third ferromagnetic layerand the second ferromagnetic layer are antiferromagnetically couple; andthe thickness and the composition of the second non-magnetic layer and athickness and a composition of the non-magnetic layer are selected sothat interlayer exchange coupling between the second ferromagnetic layerand the third ferromagnetic layer is stronger than interlayer exchangecoupling between the first ferromagnetic layer and the secondferromagnetic layer.
 15. The method of claim 10, wherein the oxide layeris a tunnel barrier layer comprising MgO, further comprising a referenceferromagnetic layer on the tunnel barrier layer, wherein the magneticdevice is a magnetic tunnel junction.
 16. The method of claim 15,wherein the reference ferromagnetic layer comprises a syntheticantiferromagnet.
 17. The method of claim 10, further comprising:controlling, by the write controller, the voltage source to output abias voltage configured to enable stable bi-directional or randomtelegraphic switching of the magnetic orientation of the secondferromagnetic layer or third ferromagnetic layer at room temperature.18. A random bit stream generator comprising: a magnetic devicecomprising: a layer stack comprising: a first ferromagnetic layer; anon-magnetic spacer layer on the first ferromagnetic layer, wherein thenon-magnetic spacer layer comprises at least one of Ru, Ir, Ta, Cr, W,Mo, Re, Hf, Zr, or V; a second ferromagnetic layer on the non-magneticspacer layer; an oxide layer on the second ferromagnetic layer; avoltage source configured to apply a bias voltage across the layer stackto cause switching of a magnetic orientation of the second ferromagneticlayer without application of an external magnetic field or a current,wherein a thickness and composition of the non-magnetic spacer layer isselected to enable a switching direction of the magnetic orientation ofthe second ferromagnetic layer to be controlled by a sign of the biasvoltage.